15.9.16 problem 30

Internal problem ID [3073]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 30
Date solved : Monday, January 27, 2025 at 07:19:11 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{3 x}+c_2 \,{\mathrm e}^{x}+c_3 \,{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 25

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (e^x \left (c_3 e^x+c_2\right )+c_1\right ) \]